Problem: Rewrite as a simplified fraction. ${1.2\overline{6} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 126.6666...\\ 10x &= 12.6666...\end{align*}}$ Subtracting the two equations, we have: ${90x = 114}$ ${x = \dfrac{114}{90}} $ ${x = \dfrac{19}{15}} \text{or} {1 \dfrac{4}{15}}$